Question

三角函数

cos40度，cos77度，cos5度，sin39度sin71度，tan66度，要求给出估值，怎么估，给出过程

Answer 1

在[0,pi]之间，cos值从1变成0，所以cos5>cos44>cos77
cos5=1, cos44=cos45=根号2/2, cos77=1
以此类推

Answer 2

1=cos0°>cos40°>cos45°=√2/2 cos40°≈0.8
1/2=cos60°>cos77°>cos90°=0 cos77°≈0.25
1=cos0°>cos5°>cos30°=√3/2 cos5°≈0.9
sin39°sin71°=sin(30°+19°)sin(90°-19°)
=(sin30°cos19°+cos30°sin19°)cos19°
=1/2(cos19°)^2+√3/2sin19°cos19°
=1/4(cos38°+1)+√3/4sin38°
=1/2(1/2cos38°+√3/2sin38°)+1/4
=1/2sin(38°+30°)+1/4
=1/2sin68°+1/4
∵√3/2=sin60°<sin68°<sin90°=1
∴sin68°≈0.9
sin39°sin71°≈1/2*0.9+1/4=0.7
√3=tan60°<tan66°<tan90°=+∞
tan66°≈2.0

Answer 3